Extended crystals

For the smaller particles which Include only a few tens or hundreds of atoms, any twinning or faulting reduces the range of ordering to the extent that the pattern can not be Interpreted In the same way as a pattern from an extended crystal. The Individual single-crystal regions may contain only two or three atomic planes. Interpretation can be made only by calculation of patterns from postulated models for the configurations of atoms (22). 

The cytoplasmic domains reconstructed from negatively stained [90] and from frozen-hydrated samples [91,177] have similar shapes. Both include the protruding lobe and the bridge region that links the Ca " -ATPase molecules into dimers. The intramembranous peptide domains of the two ATPase molecules which make up a dimer spread apart as they pass through the bilayer toward the luminal side of the membrane, establishing contacts with the Ca -ATPase molecules in the neighboring dimer chains. The lateral association of dimer chains into extended crystal lattice is... 

The atoms in a crystalline substance occupy positions in space that can be referenced to lattice points, which crystallographers refer to as the asymmetric unit (physicists call it the basis). Lattice points represent the smallest repeating unit, or chemical point group. For example, in NaCl, each Na and Cl pair may be represented by a lattice point. In structures that are more complex, a lattice point may represent several atoms (e.g., polyhedra) or entire molecules. The repetition of lattice points by translations in space forms a space lattice, representing the extended crystal structure. 

I lGURK 20-2 The body-centered cubic structure. The central atom sits at the center of a cube formed by k,r. its eight nearest neighbors, shaded to distinguish them, though every atom and its environment (in the extended crystal) is identical. The six second neighbors lie a distance 15 percent further away. We construct a Bloch sum with wave number in the z-direction, giving phase factors shown for atoms in each plane of constant z. 

The results are presented in terms of bibliographic and chemical text, 2D chemical diagrams, 3D structure diagrams at the molecular or extended crystal structure levels, and also as tables of geometrical parameters for each located substructure or chemical fragment. The search query is via... 

The smallest repeating unit of an extended crystal lattice is known as the unit cell, which governs the symmetry and structure of the overall bulk crystal. Oftentimes, it is possible to define a number of possible repeat units for a crystal lattice (Figure 2.6). The proper selection of a unit cell represents the smallest repeatable unit that possesses the same symmetry elements of the bulk crystal, and if translated along the x, y, and z axes, will generate the entire extended crystal lattice. 

The d notation indicates a diamond glide plane, found in diamond or zinc blende extended crystal structures. Whereas ghde planes are found in many inorganic-based crystals, screw axes are found predominantly in protein structures. 

The electronic properties of the extended crystal structures and the free building blocks have been compared. As free building blocks the linkers were represented in their dicarboxylate forms and the connector was considered as a part of the ZnO (wurtzite) crystal saturated with H atoms. 

Ionic compounds form extended crystal lattices that maximize the positive and negative electrostatic interactions. In NaCl, each positively charged Na ion is surrounded by six negatively charged Cl ions, and each d ion is surrounded by six Na" ions. 

There Is an extensive literature relating to Infrared studies of CO on supported platinum. However, there is no consistent band pattern or interpretations which can lead to unambiguous assignments for bands in the 2060-2085 cm region as seen in Figure 3. The various interpretations can be divided into those which emphasize the physical state of the supported metal, i.e., particle size and those which attribute small difference in band positions to chemical factors such as the presence of oxygen. On a 10% Pt/Al203, Barth ec al. [8] observed bands at 2060 and 2083 cm. They attribute the 2060 cin band to small particles which do not have extended crystal faces and the 2083 cm band to CO... 

In summary, microscopic and thermal observations of PET samples coalesced from their crystalline y-CD-IC suggest crystalline characters and melt-crystallized morphologies that are different from normal samples. After coalescence of their segregated, extended chains from the narrow channels of the crystalline inclusion complex formed with host y-CD, PET chains are much more readily crystalliz-able, and, locally, quickly form small, possibly chain-extended crystals. In addition, the noncrystalline regions of coalesced PET exhibit conformational and motional... 

Crystal size Extended crystals in pulling directions, mm up to cm dimensions perpendicular to pulling direction 100 pm up to 1 mm range... 

MolXtl molecular graphics for small molecule crystallography, D. W. Bennett, J. Appl. Crystallogr., 2004, 37, 1038 OLEX new software for visualization and analysis of extended crystal structures, O. V. Dolomanov,... 

A specification of the actual form of Bloch functions in terms of atomic orbitals is needed. They can be written as a product of a plane wave and a function, 2(r, A), with the translational periodicity of the lattice. With the Schrodinger problem written in A-dependent form, the solutions take the form of a linear combination of Bloch functions, whose coefficients are to be determined. For all the atomic orbitals %j r- rj) in the unit cell, each centered at position r -, in a crystal with N unit cells, a combination which has the same translational periodicity as the lattice is the replacement of a single AO in the reference cell with a sum over all transla-tionally equivalent AOs in the extended crystal. The final form of the crystal orbitals is then ... 

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